Figure REF  shows the shapes of the KH modes considered as the initial solution of PFE for \(St=0.4\)  and \(0.7\) . Overall, the shapes of the solutions are similar to the ones presented in [1]}, with the effects of the modulation observed mainly around the centreline. Comparing figures REF (a) and (b), it seems that the lower frequency is more affected by modulation components associated with higher harmonics; this is confirmed in figure REF (c), where the streamwise velocity fluctuations at the centreline are shown. It is also clear that the modulation wavenumbers for both frequencies are exactly the same, which is a consequence of the ansatz used in the formulation. Figure REF  also suggests that, even though there is a modulation for both frequencies, this modulation is fairly weak at the initial step.
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